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\section{Making Optimal Decisions}
\label{sec:opt}
Before we start making optimal decisions, we must first define the term
``optimal''. In order to maximize the organization's profits, we would like to
solicit the subset of examples for whom a direct mailing would result in a 
donation above $\$0.68$, which is the cost of a solicitation, but who would 
not donate without being solicited. This would maximize profits with respect 
to direct mailing soliciations. Soliciting those who will not donate an amount 
greater than the solicitaion cost incurs a negative profit and soliciting those who 
would donate irrespective of solicitation would result in wasting $\$0.68$.
However, 
sending a solicitation to those who would not donate unless solicited, 
increases the profit of the organization. Ideally, we would designate this 
set of examples as optimal.

However, this form of optimality is too ideal given our data set. The
training data does not directly give us the information about whether a 
prospective donor would donate if they received a direct mailing solicitation. 
Given this constraint, we adapt our definition of optimality to solicit anybody 
who is predicted to donate an amount greater than $\$0.68$. Since our estimation 
is the best information known about the prospective donor in the given 
circumstance, soliciting these examples would be optimal. We will aspire for
this definition of optimality.


